2011 AMC 10A Problem 15

Below is the professionally curated solution for Problem 15 of the 2011 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 10A solutions, or check the answer key.

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Concepts:rate linear equation

Difficulty rating: 1370

15.

Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first $40$ miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of $0.02$ gallons per mile. On the whole trip he averaged $55$ miles per gallon. How long was the trip in miles?

$140$

$240$

$440$

$640$

$840$

Solution:

Let $x$ be the distance the car drove solely on gasoline. We have that $\dfrac{40 + x}{0.02x} = 55.$ Cross-multiplying and simplifying gives $40 = .1x$ $x = 400.$ The total length of the trip is then $400 + 40 = 440.$

Thus, C is the correct answer.

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